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An oceanfront town is considering ways to reduce littering on its beaches. It currently has a fine for littering of 100. It does not currently patrol the beaches to try to catch anyone littering so it estimates the probability of someone littering is caught is .001. Suppose that anyone who is caught is convicted. Further, assume that the reason people litter is they don't want to walk to a trash can on the beach, which costs 2 in effort. Additionally, assume that potential litterers are rational and respond to expected costs and benefits.
(a) If the town leaves the fine unchanged, to what value does it need to raise the probability of someone who litters being caught?
(b) If the town does not change the probability that someone who litters is caught, how large must the fine be to deter littering?
(c) Suppose the town assigns police officers to patrol the beaches and estimates that the probability that someone who litters is caught is now .04. Will this deter littering? Explain.
(d) Suppose the mayor is opposed to new expenditures and to have police officers patrol the beaches will require paying overtime. Based on this, would she prefer to impose the fine found in part b)? Explain.
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